Immigration & The Economic Crisis
We are now seeing several examples of this, the most notable being the United States and Ireland.
First of all, the U.S. Census Bureau estimates that for the first time in a long time, the number of foreign born has actually dropped somewhat. To be sure, because so many immigrants are in America illegally and because we can't know for sure the number of illegal immigrants, this estimate has a significant statistical margin of error, big enough to make it possible that there was a small rise. But there could have also been an even bigger drop, and there's little doubt that the number of new immigrants have dropped significantly and that the number of immigrants that return to their country of origin has increased.
The reason why the economic slump should reduce immigration is because it reduces job opportunities and so makes it more difficult for immigrants to get jobs. It is true that the slump has worsened job opportunities in the countries of origin too, but because [employment based] immigration requires a job in the new country, worsening job prospects will reduce immigration even if the job markets gets worse in both countries.
Also, immigrants have been over represented as workers in the construction industry, "Ground Zero" in the economic crisis. This means that job prospects for immigrants have deteriorated even more than for natives.
A similar trend can be seen in Ireland. In the year to April 2009, net migration was for the first time since the year to April 1995 negative. In 2006, net immigration was as 72,000, the equivalent of more than 5 million in America, and in 2007 the number was only slightly lower. By 2008, the number had been cut into almost half (38,500) and by 2009 it was a negative 7,800.
The group that accounted for most of the swing was people from EU12, which is to say the 12 new EU member countries in Eastern Europe and the Mediterranean. In 2006, net immigration from there was 42,700 and in 2007 it was 38,500. In 2009 it was -16,600.
Contributing further to this drop has been that Poland, the biggest country of origin among EU12 immigrants, has had a much stronger economy than the rest of Europe.
Note however that this logic is primarily applicable to labor force migration. Immigration based on asylum applications or marriage/family relations is likely to be a lot less affected by this factor.
Incidentally, it could be noted that the relatively high level of immigration during the boom and the [at least so far] more limited degree of emigration during the bust implies that labor immobility really isn't such a strong factor in Europe as many opponents of the European Monetary Union have claimed.